A fitness center is hosting a special promotion for group classes. The center can accommodate a maximum of 200 participants. The center is offering two types of classes: yoga (Y) and spin (S). Each yoga class requires 5 participants to run, while each spin class requires 10 participants.

Question

2. The center schedules 6 yoga classes and 8 spin classes. Using the inequality created in part 1 determine if this schedule meets the participant's capacity.

Answer 1

To determine if the fitness center's schedule meets the participant capacity, we need to calculate the total number of participants required for both yoga and spin classes based on the given information.

1. Yoga Classes:

   • Each yoga class requires 5 participants.
   • The center is scheduling 6 yoga classes.
   • Total participants for yoga = Number of yoga classes × Participants per yoga class \[ \text{Total yoga participants} = 6 \text{ classes} \times 5 \text{ participants/class} = 30 \text{ participants} \]

2. Spin Classes:

   • Each spin class requires 10 participants.
   • The center is scheduling 8 spin classes.
   • Total participants for spin = Number of spin classes × Participants per spin class \[ \text{Total spin participants} = 8 \text{ classes} \times 10 \text{ participants/class} = 80 \text{ participants} \]

3. Total Participants:

   • Total participants required for both classes = Total yoga participants + Total spin participants \[ \text{Total participants} = 30 \text{ (from yoga)} + 80 \text{ (from spin)} = 110 \text{ participants} \]

4. Capacity Check:

   • The maximum capacity of the fitness center is 200 participants.
   • Since 110 participants is less than the maximum capacity of 200 participants, the schedule meets the participant's capacity.

Therefore, the answer is that yes, the schedule of 6 yoga classes and 8 spin classes meets the participant capacity, allowing for 110 participants out of a maximum of 200.